The electrodynamics of topological insulators (TIs) is described by modified Maxwell's equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e2/2hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.

In contrast to well studied multiferroic manganites with a spiral structure, the electric polarization in multiferroic borates is induced within collinear antiferromagnetic structure and can easily be switched by small static fields. Because of specific symmetry conditions, static and dynamic properties in borates are directly connected, which leads to giant magnetoelectric and magnetodielectric effects. Here we prove experimentally that the giant magnetodielectric effect in samarium ferroborate SmFe3(BO3)4 is of intrinsic origin and is caused by an unusually large electromagnon situated in the microwave range. This electromagnon reveals strong optical activity exceeding 120 degrees of polarization rotation in a millimeter thick sample

Using electron-spin-resonance (ESR) technique we investigate the magnetic structure of CuCrO2, quasi-two-dimensional antiferromagnet with weakly distorted triangular lattice. Resonance frequencies and the excitation conditions in CuCrO2 at low temperatures are well described in the frame of cycloidal spin structure, defined by two susceptibilities parallel and perpendicular to the spin plane (χ ⊥ and χ ) and by a biaxial crystal-field anisotropy. In agreement with the calculations, the character of the eigenmodes changes drastically at the spin-flop transition. The splitting of the observed modes can be well attributed to the resonances from different domains. The domain structure in CuCrO2 can be controlled by annealing of the sample in magnetic field.

The universal value of Faraday rotation angle close to the fine structure constant (α ≈ 1/137) is experimentally observed in thin HgTe quantum wells with thickness on the border between trivial insulating and the topologically non-trivial Dirac phases. The quantized value of the Faraday angle remains robust in the broad range of magnetic fields and gate voltages. Dynamic Hall conductivity of the hole-like carriers extracted from the analysis of the transmission data shows theoretically predicted universal value of σxy = e 2 /h consistent with the doubly degenerate Dirac state. On shifting the Fermi level by the gate voltage the effective sign of the charge carriers changes from positive (holes) to negative (electrons). The electron-like part of the dynamic response does not show quantum plateaus and is well described within the classical Drude model. PACS numbers:The strong spin-orbit coupling and an inverted band structure in mercury telluride makes this material to a nearly universal tool to probe novel physical effects with the film thickness being a tuning parameter [1,2]. If the thickness of HgTe wells is below critical, d < d c ≈ 6.3 nm, the sequence of the conduction and valence bands is conventional and a trivial insulating state is realized. For thicker films and in the bulk mercury telluride the inversion of valence and conduction bands leads to topologically non-trivial surface states [3,4]. This state is characterised by the locking of the electron spin and the electron momentum and they are topologically protected against non-magnetic impurity scattering.If the thickness of HgTe well is equal to critical, the gap between valence and conduction bands disappears and a two-dimensional (2D) electron gas is formed with Dirac cone dispersion [1,2]. Close to the center of the Dirac cone the electron spin is not a good quantum number, but has to be replaced by pseudo-spin or helicity [3,5]. Due to the particle-hole symmetry of these states, the quantum Hall effect becomes shifted by a half-integer and takes the form σ xy = γ(n+1/2)e 2 /h. In well-investigated case of graphene [6,7] the states are fourfold degenerate, i.e. γ = 4, as two Dirac cones are present in the Brillouin zone which are both doubly spin-degenerate.Magneto-optics in the terahertz range has been proven to be an effective tool to investigate two-dimensional conducting states in several quantum systems, like graphene [8-10], Bi 2 Se 3 [11][12][13][14], and HgTe [15][16][17][18][19][20][21][22]. Magneto-optical spectroscopy has the advantages of being contact-free and of directly accessing the effective mass m c via the cyclotron resonance Ω c = eB/m c . Here B is the external magnetic field.In the dynamical regime the unusual character of the quantum Hall effect in systems with Dirac cones can be shown [23][24][25][26] to lead to a universal values of the Faraday and Kerr rotation with θ F = α ∼ 1/137 and θ K = π/2, respectively. Such predictions have been recently confirmed experimentally in graphene [9], where the Faraday angle is additio...

Electric manipulation of magnetic properties is a key problem of materials research. To fulfil the requirements of modern electronics, these processes must be shifted to high frequencies. In multiferroic materials this may be achieved by electric and magnetic control of their fundamental excitations. Here we identify magnetic vibrations in multiferroic iron-borates which are simultaneously sensitive to external electric and magnetic fields. Nearly 100 % modulation of the terahertz radiation in an external field is demonstrated for SmFe3(BO3)4. High sensitivity can be explained by a modification of the spin orientation which controls the excitation conditions in multiferroic borates. These experiments demonstrate the possibility to alter terahertz magnetic properties of materials independently by external electric and magnetic fields.

All-electrical control of a dynamic magnetoelectric effect is demonstrated in a classical multiferroic manganite DyMnO3, a material containing coupled antiferromagnetic and ferroelectric orders. Due to intrinsic magnetoelectric coupling with electromagnons a linearly polarized terahertz light rotates upon passing through the sample. The amplitude and the direction of the polarization rotation are defined by the orientation of ferroelectric domains and can be switched by static voltage. These experiments allow the terahertz polarization to be tuned using the dynamic magnetoelectric effect.PACS numbers: 75.85.+t, 78.20.Jq, 78.20.Ek, 75.30.Ds Electric and magnetic field control of the propagation and the polarization state of terahertz radiation is one of the prerequisites for continuous progress of modern electronics. A number of recent developments in this direction have been achieved using multiferroics, i.e. materials simultaneously revealing electric and magnetic ordering [1][2][3][4][5]. Several multiferroics provide not only a direct coupling between static electric and magnetic properties but also give a possibility to modify dynamic susceptibilities by external fields. Application of a static magnetic field to the multiferroic materials leads to dichroism in the terahertz range [6,7] or even to more complex effects like controlled chirality [8] or directional dichroism [9][10][11]. Electric control of terahertz radiation is more difficult to realize and it has been recently demonstrated in Raman scattering experiments [12].Dynamical properties of several multiferroic materials in the terahertz range are governed by novel magnetoelectric modes called electromagnons [13][14][15][16]. Electromagnons may be defined as collective excitations of the magnetic structure which are coupled to the electric dipole moment.They may be regarded as a mixture of magnons and phonons. In orthorhombic rare earth manganites RMnO 3 one generally observes several electromagnons in the terahertz and sub-terahertz range. A strong high frequency mode around 2-3 THz is well understood on the basis of a symmetric Heisenberg exchange (HE) coupling [17,18] as a zone edge magnon which can be excited by electric component of the electromagnetic radiation. A second intensive mode existing at 0.5-1 THz has been explained using the same mechanism but including a Brillouin zone folding due to modulation of the magnetic cycloid [18,19]. In the sub-terahertz frequency range a series of weaker modes is observed in optical [14,20] and neutron scattering experiments [21]. These modes are explained as the magnetic eigenmodes of the spin cycloid in RMnO 3 . Some of these modes may get an electrical dipole activity due to the relativistic Dzyaloshinskii-Moriya (DM) mechanism. Dynamic contributions due to this mechanism have been investigated both experimentally and theoretically [20,[22][23][24][25]. In spite of its weakness, the DM interaction is a promising mechanism especially in application to spiral magnets as it connects static spontaneous ...

One of the most fascinating and counter-intuitive recent effects in multiferroics is the directional anisotropy, the asymmetry of light propagation with respect to the direction of propagation. In such case the absorption in a material can be different for opposite directions. Beside absorption, different velocities of light for different directions of propagation may be also expected, which is termed directional birefringence. In this work, we demonstrate large directional anisotropy in a multiferroic samarium ferroborate. The effect is observed for linear polarization of light in the range of millimeter-wavelengths, and it survives down to low frequencies. The dispersion and absorption close to the electromagnon resonance can be controlled by external magnetic field and is fully suppressed in one direction. By changing the geometry of the external field, samarium ferroborate shows giant optical activity, which makes this material to a universal tool for optical control: with a magnetic field as an external parameter it allows switching between two functionalities: polarization rotation and directional anisotropy.

Terahertz properties of mercury telluride (HgTe) films with critical thickness are presented and discussed. The density of the charge carriers is controlled using contact-free optical doping by visible light. In the magneto-optical response of HgTe the contribution of two types of carriers (electrons and holes) can be identified. The density of the electrons can be modified by light illumination by more than one order of magnitude. As the hole density is roughly illuminationindependent, the terahertz response of the illuminated samples becomes purely electronic. In some cases, light illumination may switch the qualitative electrodynamic response from hole-like to the electron-like. The cyclotron mass of the electrons could be extracted from the data and shows a square root dependence upon the charge concentration in the broad range of parameters. This can be interpreted as a clear proof of a linear dispersion relations, i.e. Dirac-type charge carriers.